Question

How many partitions of closed interval [a,b] are
possible?
a. finite
b. one and only one
c. infinite
d. b-a​

Answer 1

Answer:

ans is number b

Step-by-step explanation:

number b is right

Answer 2

Answer:

For a closed interval,finite partitions are possible. Therefore, the correct answer would be a. finite.

Step-by-step explanation:

A partition of a closed bounded interval [a, b] is a finite subset P ⊂ [a, b] that consists of the endpoints a and b.

Let x₀, x₁, . . . , x be the listing of all factors of P and that too ordered so that x₀ < x₁ < · · · < x (observe that x₀ = a and x = b).

These factors break up the interval [a, b] into finitely many sub-intervals [x₀, x₁], [x₁, x₂], . . . , [x₋₁, x]. The norm of the partition P, denoted ||P||, is the most of lengths of those sub-intervals: ||P|| = $max_{1 < j < x}$ |xj − xj₋₁|.

Given  walls P and Q of the equal interval, we say that Q is a refinement of P (or that Q is finer than P) if P ⊂ Q. Observe that P ⊂ Q implies ||Q|| ≤ ||P||.

For any  walls P and Q of the interval [a, b], the union P ∪ Q is likewise a partition that refines each P and Q.